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test_steadystate.py
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test_steadystate.py
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# This file is part of QuTiP: Quantum Toolbox in Python.
#
# Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
# of its contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
# PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
from qutip import *
from numpy import linspace
from numpy.testing import assert_, assert_equal, run_module_suite
def test_qubit():
"Steady state: Thermal qubit"
# thermal steadystate of a qubit: compare numerics with analytical formula
sx = sigmax()
sz = sigmaz()
sm = destroy(2)
H = 0.5 * 2 * pi * sz
gamma1 = 0.05
wth_vec = linspace(0.1, 3, 20)
p_ss = zeros(shape(wth_vec))
for idx, wth in enumerate(wth_vec):
n_th = 1.0 / (exp(1.0 / wth) - 1) # bath temperature
c_op_list = []
rate = gamma1 * (1 + n_th)
c_op_list.append(sqrt(rate) * sm)
rate = gamma1 * n_th
c_op_list.append(sqrt(rate) * sm.dag())
rho_ss = steadystate(H, c_op_list)
p_ss[idx] = expect(sm.dag() * sm, rho_ss)
p_ss_analytic = exp(-1.0 / wth_vec) / (1 + exp(-1.0 / wth_vec))
delta = sum(abs(p_ss_analytic - p_ss))
assert_equal(delta < 1e-5, True)
def test_ho():
"Steady state: Thermal harmonic oscillator"
# thermal steadystate of an oscillator: compare numerics with analytical
# formula
a = destroy(40)
H = 0.5 * 2 * pi * a.dag() * a
gamma1 = 0.05
wth_vec = linspace(0.1, 3, 20)
p_ss = zeros(shape(wth_vec))
for idx, wth in enumerate(wth_vec):
n_th = 1.0 / (exp(1.0 / wth) - 1) # bath temperature
c_op_list = []
rate = gamma1 * (1 + n_th)
c_op_list.append(sqrt(rate) * a)
rate = gamma1 * n_th
c_op_list.append(sqrt(rate) * a.dag())
rho_ss = steadystate(H, c_op_list)
p_ss[idx] = real(expect(a.dag() * a, rho_ss))
p_ss_analytic = 1.0 / (exp(1.0 / wth_vec) - 1)
delta = sum(abs(p_ss_analytic - p_ss))
assert_equal(delta < 1e-3, True)
def test_driven_cavity():
"Steady state: Driven cavity"
N = 30
Omega = 0.01 * 2 * pi
Gamma = 0.05
a = destroy(N)
H = Omega * (a.dag() + a)
c_ops = [sqrt(Gamma) * a]
rho_ss = steadystate(H, c_ops)
rho_ss_analytic = coherent_dm(N, -1.0j * (Omega)/(Gamma/2))
assert_((rho_ss - rho_ss_analytic).norm() < 1e-4)
if __name__ == "__main__":
run_module_suite()